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2 years ago

5

Rodney has a board 5/6 yd long. He used 1/5 of the board to make a frame. How long is the board used to make the frame.

1 answer:

Katarina [22]2 years ago

3 0

He uses 1/5 OF 5/6 of a yard. That "of" is very important, because it indicates that, to find the answer, you multiply the two together.

That being said (1/5) times (5/6) =5/30, which can be reduced to 1/6 yds to make the frame

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Function f is an exponential function. It predicts the value of a famous painting, in thousands of dollars, as a function of the

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Answer:

$y=8 \cdot (\frac{5}{4})^x$

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or

$f(x)=8 \cdot (1.25)^x$

Step-by-step explanation:

We are going to see if the exponential curve is of the form:

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If you are given the $y-$ intercept, then $a$ is easy to find.

It is just the $y-$ coordinate of the $y-$ intercept is your value for $a$ .

(Why? The $y-$ intercept happens when $x=0$ . Replacing $x$ with 0 gives $y=a \cdot b^0=a \cdot 1=a$ . This says when $x=0 \text{ that} y=a$ .)

So $a=8$ .

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Let's do this.

We are given $(1,10)$ is a point on our curve.

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So the equation if it works out for the other point given is:

$y=8 \cdot (\frac{5}{4})^x$

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This says when $x=2$ , $y=12.5$ .

Let's replace $x$ with 2 and see what we get for $y$ :

$y=8 \cdot (\frac{5}{4})^2$

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$y=\frac{25}{2}$

$y=12.5$

So we are good. We have found an equation satisfying all 3 points given.

The equation is $y=8 \cdot (\frac{5}{4})^x$ .

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